正弦倍角的投影
Author: 藍邦偉　老師

比較y=sinx與y=sin2x圖形的變化

2θ

y=sin(2x)

y=sinx

θ

K: (0.0, y((Corner[1.0] + 2.0 * Corner[4.0]) / 3.0))
A = (-1.5707963267948966, 0)
c = Circle(A, 1.0)
B = Point(c)
θ = 0.2617993877991494 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
B' = Rotate(B, 2.0 * θ, A)
a = Segment(A, B')
b(x) = sin(2.0 * x)
d = OrthogonalLine(B', xAxis)
C: (-(3.141592653589793) / 2.0 + cos(2.0 * θ), 0.0)
e = Segment(B', C)
α = Angle(B, A, B')
P: (θ, sin(2.0 * θ))
f = OrthogonalLine(P, xAxis)
T_1 = Corner(1.0)
T_4: (Corner[4.0] + Corner[1.0]) / 2.0
T_2 = Corner(2.0)
T_3: (Corner[3.0] + Corner[2.0]) / 2.0
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
h = Segment(T_3, T_4)
T_{y1}: (x((2.0 * Corner[3.0] + 5.0 * Corner[4.0]) / 7.0), y(T_3))
T_{y2}: (2.0 * Corner[3.0] + 5.0 * Corner[4.0]) / 7.0
v_1 = Vector(T_{y1}, T_{y2})
T_{y3}: (x((2.0 * Corner[3.0] + 5.0 * Corner[4.0]) / 7.0), y(Corner[1.0]))
v_2 = Vector(T_{y3}, T_{y1})
T_{y4}: (7.0 * T_{y3} + 3.0 * T_{y1}) / 10.0
v = Vector((x(Corner[1.0]), y(T_{y4})), (x(Corner[2.0]), y(T_{y4})))
u = Vector((x(Corner[1.0]), y(K)), (x(Corner[2.0]), y(K)))
i = OrthogonalLine(A, u)
A_{0}: (-(3.141592653589793 / 2.0), y(T_{y4}))
k = Circle(A_{0}, 1.0)
B_0: A_{0} + (1.0, 0.0)
E = Rotate(B_0, θ, A_{0})
j = Segment(A_{0}, E)
F: (x(E), y(A_{0}))
l = Segment(E, F)
β = Angle(B_0, A_{0}, E)
K': A_{0} + (3.141592653589793 / 2.0, 0.0)
D: (θ, 0.0)
m = Segment(P, D)
n: x = x(E)
p: y = y(B')
q: y = y(E)
P_0: (θ, y(E))
g(x) = sin(x) + y(T_{y4})
P_1: (θ, y(K'))
r = Segment(P_0, P_1)